%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC412-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 02:41:08 PM UTC 2026
% Result : Unsatisfiable 0.15s 15.42s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 55
% Syntax : Number of formulae : 154 ( 9 unt; 18 def)
% Number of atoms : 467 ( 119 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 550 ( 237 ~; 295 |; 0 &)
% ( 18 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 22 ( 20 usr; 19 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 11 con; 0-2 aty)
% Number of variables : 126 ( 126 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f73,axiom,
! [U] :
( app(U,nil) = U
| ~ ssList(U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f85,axiom,
! [U,V] :
( ssList(app(V,U))
| ~ ssList(V)
| ~ ssList(U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f118,axiom,
! [U,V] :
( nil = U
| ~ ssList(U)
| ~ ssList(V)
| app(U,V) != nil ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f119,axiom,
! [U,V] :
( nil = V
| ~ ssList(U)
| ~ ssList(V)
| app(U,V) != nil ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f190,negated_conjecture,
sk2 = sk4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f191,negated_conjecture,
sk1 = sk3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f192,negated_conjecture,
! [A,B,C,D,E,F] :
( app(app(cons(D,nil),F),cons(E,nil)) != sk4
| app(app(cons(E,nil),F),cons(D,nil)) = sk3
| ~ ssList(F)
| ~ ssItem(E)
| ~ ssItem(D)
| app(app(cons(A,nil),cons(B,nil)),C) != sk4
| ~ ssList(C)
| ~ ssItem(B)
| ~ ssItem(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f197,negated_conjecture,
! [A,B,C] :
( ssItem(sk11)
| app(app(cons(A,nil),cons(B,nil)),C) != sk4
| ~ ssList(C)
| ~ ssItem(B)
| ~ ssItem(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f198,negated_conjecture,
! [A,B,C] :
( ssItem(sk12)
| app(app(cons(A,nil),cons(B,nil)),C) != sk4
| ~ ssList(C)
| ~ ssItem(B)
| ~ ssItem(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f199,negated_conjecture,
! [A,B,C] :
( ssList(sk13)
| app(app(cons(A,nil),cons(B,nil)),C) != sk4
| ~ ssList(C)
| ~ ssItem(B)
| ~ ssItem(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f200,negated_conjecture,
! [A,B,C] :
( app(app(cons(sk11,nil),sk13),cons(sk12,nil)) = sk2
| app(app(cons(A,nil),cons(B,nil)),C) != sk4
| ~ ssList(C)
| ~ ssItem(B)
| ~ ssItem(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f201,negated_conjecture,
! [A,B,C] :
( app(app(cons(sk12,nil),sk13),cons(sk11,nil)) != sk1
| app(app(cons(A,nil),cons(B,nil)),C) != sk4
| ~ ssList(C)
| ~ ssItem(B)
| ~ ssItem(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f202,negated_conjecture,
! [A,B,C] :
( app(app(cons(A,nil),C),cons(B,nil)) != sk4
| app(app(cons(B,nil),C),cons(A,nil)) = sk3
| ~ ssList(C)
| ~ ssItem(B)
| ~ ssItem(A)
| ssItem(sk5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f203,negated_conjecture,
! [A,B,C] :
( app(app(cons(A,nil),C),cons(B,nil)) != sk4
| app(app(cons(B,nil),C),cons(A,nil)) = sk3
| ~ ssList(C)
| ~ ssItem(B)
| ~ ssItem(A)
| ssItem(sk6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f204,negated_conjecture,
! [A,B,C] :
( app(app(cons(A,nil),C),cons(B,nil)) != sk4
| app(app(cons(B,nil),C),cons(A,nil)) = sk3
| ~ ssList(C)
| ~ ssItem(B)
| ~ ssItem(A)
| ssList(sk7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f205,negated_conjecture,
! [A,B,C] :
( app(app(cons(A,nil),C),cons(B,nil)) != sk4
| app(app(cons(B,nil),C),cons(A,nil)) = sk3
| ~ ssList(C)
| ~ ssItem(B)
| ~ ssItem(A)
| app(app(cons(sk5,nil),cons(sk6,nil)),sk7) = sk2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f210,negated_conjecture,
( ssItem(sk11)
| ssItem(sk5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f211,negated_conjecture,
( ssItem(sk12)
| ssItem(sk5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f212,negated_conjecture,
( ssList(sk13)
| ssItem(sk5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f213,negated_conjecture,
( app(app(cons(sk11,nil),sk13),cons(sk12,nil)) = sk2
| ssItem(sk5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f214,negated_conjecture,
( app(app(cons(sk12,nil),sk13),cons(sk11,nil)) != sk1
| ssItem(sk5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f227,negated_conjecture,
( ssItem(sk11)
| ssItem(sk6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f228,negated_conjecture,
( ssItem(sk12)
| ssItem(sk6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f229,negated_conjecture,
( ssList(sk13)
| ssItem(sk6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f230,negated_conjecture,
( app(app(cons(sk11,nil),sk13),cons(sk12,nil)) = sk2
| ssItem(sk6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f231,negated_conjecture,
( app(app(cons(sk12,nil),sk13),cons(sk11,nil)) != sk1
| ssItem(sk6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f232,negated_conjecture,
( ssItem(sk11)
| ssList(sk7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f233,negated_conjecture,
( ssItem(sk11)
| app(app(cons(sk5,nil),cons(sk6,nil)),sk7) = sk2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f234,negated_conjecture,
( ssItem(sk12)
| ssList(sk7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f235,negated_conjecture,
( ssList(sk13)
| ssList(sk7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f236,negated_conjecture,
( app(app(cons(sk11,nil),sk13),cons(sk12,nil)) = sk2
| ssList(sk7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f237,negated_conjecture,
( app(app(cons(sk12,nil),sk13),cons(sk11,nil)) != sk1
| ssList(sk7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f238,negated_conjecture,
( ssItem(sk12)
| app(app(cons(sk5,nil),cons(sk6,nil)),sk7) = sk2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f239,negated_conjecture,
( ssList(sk13)
| app(app(cons(sk5,nil),cons(sk6,nil)),sk7) = sk2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f240,negated_conjecture,
( app(app(cons(sk11,nil),sk13),cons(sk12,nil)) = sk2
| app(app(cons(sk5,nil),cons(sk6,nil)),sk7) = sk2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f241,negated_conjecture,
( app(app(cons(sk12,nil),sk13),cons(sk11,nil)) != sk1
| app(app(cons(sk5,nil),cons(sk6,nil)),sk7) = sk2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f249,plain,
ssList(nil),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f315,plain,
! [X0] :
( app(X0,nil) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f73]) ).
fof(f327,plain,
! [X0,X1] :
( ssList(app(X1,X0))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f85]) ).
fof(f368,plain,
! [U] :
( nil = U
| ~ ssList(U)
| ! [V] :
( ~ ssList(V)
| app(U,V) != nil ) ),
inference(miniscoping,[status(thm)],[f118]) ).
fof(f369,plain,
! [X0,X1] :
( nil = X0
| ~ ssList(X0)
| ~ ssList(X1)
| app(X0,X1) != nil ),
inference(cnf_transformation,[status(thm)],[f368]) ).
fof(f370,plain,
! [V] :
( nil = V
| ! [U] :
( ~ ssList(U)
| ~ ssList(V)
| app(U,V) != nil ) ),
inference(miniscoping,[status(thm)],[f119]) ).
fof(f371,plain,
! [X0,X1] :
( nil = X1
| ~ ssList(X0)
| ~ ssList(X1)
| app(X0,X1) != nil ),
inference(cnf_transformation,[status(thm)],[f370]) ).
fof(f476,plain,
sk2 = sk4,
inference(cnf_transformation,[status(thm)],[f190]) ).
fof(f477,plain,
sk1 = sk3,
inference(cnf_transformation,[status(thm)],[f191]) ).
fof(f478,plain,
! [D,E,F] :
( app(app(cons(D,nil),F),cons(E,nil)) != sk4
| app(app(cons(E,nil),F),cons(D,nil)) = sk3
| ~ ssList(F)
| ~ ssItem(E)
| ~ ssItem(D)
| ! [A,B,C] :
( app(app(cons(A,nil),cons(B,nil)),C) != sk4
| ~ ssList(C)
| ~ ssItem(B)
| ~ ssItem(A) ) ),
inference(miniscoping,[status(thm)],[f192]) ).
fof(f479,plain,
! [X0,X1,X2,X3,X4,X5] :
( app(app(cons(X3,nil),X5),cons(X4,nil)) != sk4
| app(app(cons(X4,nil),X5),cons(X3,nil)) = sk3
| ~ ssList(X5)
| ~ ssItem(X4)
| ~ ssItem(X3)
| app(app(cons(X0,nil),cons(X1,nil)),X2) != sk4
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f478]) ).
fof(f488,plain,
( ssItem(sk11)
| ! [A,B,C] :
( app(app(cons(A,nil),cons(B,nil)),C) != sk4
| ~ ssList(C)
| ~ ssItem(B)
| ~ ssItem(A) ) ),
inference(miniscoping,[status(thm)],[f197]) ).
fof(f489,plain,
! [X0,X1,X2] :
( ssItem(sk11)
| app(app(cons(X0,nil),cons(X1,nil)),X2) != sk4
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f488]) ).
fof(f490,plain,
( ssItem(sk12)
| ! [A,B,C] :
( app(app(cons(A,nil),cons(B,nil)),C) != sk4
| ~ ssList(C)
| ~ ssItem(B)
| ~ ssItem(A) ) ),
inference(miniscoping,[status(thm)],[f198]) ).
fof(f491,plain,
! [X0,X1,X2] :
( ssItem(sk12)
| app(app(cons(X0,nil),cons(X1,nil)),X2) != sk4
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f490]) ).
fof(f492,plain,
( ssList(sk13)
| ! [A,B,C] :
( app(app(cons(A,nil),cons(B,nil)),C) != sk4
| ~ ssList(C)
| ~ ssItem(B)
| ~ ssItem(A) ) ),
inference(miniscoping,[status(thm)],[f199]) ).
fof(f493,plain,
! [X0,X1,X2] :
( ssList(sk13)
| app(app(cons(X0,nil),cons(X1,nil)),X2) != sk4
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f492]) ).
fof(f494,plain,
( app(app(cons(sk11,nil),sk13),cons(sk12,nil)) = sk2
| ! [A,B,C] :
( app(app(cons(A,nil),cons(B,nil)),C) != sk4
| ~ ssList(C)
| ~ ssItem(B)
| ~ ssItem(A) ) ),
inference(miniscoping,[status(thm)],[f200]) ).
fof(f495,plain,
! [X0,X1,X2] :
( app(app(cons(sk11,nil),sk13),cons(sk12,nil)) = sk2
| app(app(cons(X0,nil),cons(X1,nil)),X2) != sk4
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f494]) ).
fof(f496,plain,
( app(app(cons(sk12,nil),sk13),cons(sk11,nil)) != sk1
| ! [A,B,C] :
( app(app(cons(A,nil),cons(B,nil)),C) != sk4
| ~ ssList(C)
| ~ ssItem(B)
| ~ ssItem(A) ) ),
inference(miniscoping,[status(thm)],[f201]) ).
fof(f497,plain,
! [X0,X1,X2] :
( app(app(cons(sk12,nil),sk13),cons(sk11,nil)) != sk1
| app(app(cons(X0,nil),cons(X1,nil)),X2) != sk4
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f496]) ).
fof(f498,plain,
! [X0,X1,X2] :
( app(app(cons(X0,nil),X2),cons(X1,nil)) != sk4
| app(app(cons(X1,nil),X2),cons(X0,nil)) = sk3
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0)
| ssItem(sk5) ),
inference(cnf_transformation,[status(thm)],[f202]) ).
fof(f499,plain,
! [X0,X1,X2] :
( app(app(cons(X0,nil),X2),cons(X1,nil)) != sk4
| app(app(cons(X1,nil),X2),cons(X0,nil)) = sk3
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0)
| ssItem(sk6) ),
inference(cnf_transformation,[status(thm)],[f203]) ).
fof(f500,plain,
! [X0,X1,X2] :
( app(app(cons(X0,nil),X2),cons(X1,nil)) != sk4
| app(app(cons(X1,nil),X2),cons(X0,nil)) = sk3
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0)
| ssList(sk7) ),
inference(cnf_transformation,[status(thm)],[f204]) ).
fof(f501,plain,
! [X0,X1,X2] :
( app(app(cons(X0,nil),X2),cons(X1,nil)) != sk4
| app(app(cons(X1,nil),X2),cons(X0,nil)) = sk3
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0)
| app(app(cons(sk5,nil),cons(sk6,nil)),sk7) = sk2 ),
inference(cnf_transformation,[status(thm)],[f205]) ).
fof(f506,plain,
( ssItem(sk11)
| ssItem(sk5) ),
inference(cnf_transformation,[status(thm)],[f210]) ).
fof(f507,plain,
( ssItem(sk12)
| ssItem(sk5) ),
inference(cnf_transformation,[status(thm)],[f211]) ).
fof(f508,plain,
( ssList(sk13)
| ssItem(sk5) ),
inference(cnf_transformation,[status(thm)],[f212]) ).
fof(f509,plain,
( app(app(cons(sk11,nil),sk13),cons(sk12,nil)) = sk2
| ssItem(sk5) ),
inference(cnf_transformation,[status(thm)],[f213]) ).
fof(f510,plain,
( app(app(cons(sk12,nil),sk13),cons(sk11,nil)) != sk1
| ssItem(sk5) ),
inference(cnf_transformation,[status(thm)],[f214]) ).
fof(f523,plain,
( ssItem(sk11)
| ssItem(sk6) ),
inference(cnf_transformation,[status(thm)],[f227]) ).
fof(f524,plain,
( ssItem(sk12)
| ssItem(sk6) ),
inference(cnf_transformation,[status(thm)],[f228]) ).
fof(f525,plain,
( ssList(sk13)
| ssItem(sk6) ),
inference(cnf_transformation,[status(thm)],[f229]) ).
fof(f526,plain,
( app(app(cons(sk11,nil),sk13),cons(sk12,nil)) = sk2
| ssItem(sk6) ),
inference(cnf_transformation,[status(thm)],[f230]) ).
fof(f527,plain,
( app(app(cons(sk12,nil),sk13),cons(sk11,nil)) != sk1
| ssItem(sk6) ),
inference(cnf_transformation,[status(thm)],[f231]) ).
fof(f528,plain,
( ssItem(sk11)
| ssList(sk7) ),
inference(cnf_transformation,[status(thm)],[f232]) ).
fof(f529,plain,
( ssItem(sk11)
| app(app(cons(sk5,nil),cons(sk6,nil)),sk7) = sk2 ),
inference(cnf_transformation,[status(thm)],[f233]) ).
fof(f530,plain,
( ssItem(sk12)
| ssList(sk7) ),
inference(cnf_transformation,[status(thm)],[f234]) ).
fof(f531,plain,
( ssList(sk13)
| ssList(sk7) ),
inference(cnf_transformation,[status(thm)],[f235]) ).
fof(f532,plain,
( app(app(cons(sk11,nil),sk13),cons(sk12,nil)) = sk2
| ssList(sk7) ),
inference(cnf_transformation,[status(thm)],[f236]) ).
fof(f533,plain,
( app(app(cons(sk12,nil),sk13),cons(sk11,nil)) != sk1
| ssList(sk7) ),
inference(cnf_transformation,[status(thm)],[f237]) ).
fof(f534,plain,
( ssItem(sk12)
| app(app(cons(sk5,nil),cons(sk6,nil)),sk7) = sk2 ),
inference(cnf_transformation,[status(thm)],[f238]) ).
fof(f535,plain,
( ssList(sk13)
| app(app(cons(sk5,nil),cons(sk6,nil)),sk7) = sk2 ),
inference(cnf_transformation,[status(thm)],[f239]) ).
fof(f536,plain,
( app(app(cons(sk11,nil),sk13),cons(sk12,nil)) = sk2
| app(app(cons(sk5,nil),cons(sk6,nil)),sk7) = sk2 ),
inference(cnf_transformation,[status(thm)],[f240]) ).
fof(f537,plain,
( app(app(cons(sk12,nil),sk13),cons(sk11,nil)) != sk1
| app(app(cons(sk5,nil),cons(sk6,nil)),sk7) = sk2 ),
inference(cnf_transformation,[status(thm)],[f241]) ).
fof(f545,definition,
! [X0,X1,X2] :
( sQ2_spl
<=> ( app(app(cons(X0,nil),cons(X1,nil)),X2) != sk4
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f546,plain,
! [X0,X1,X2] :
( ~ sQ2_spl
| app(app(cons(X0,nil),cons(X1,nil)),X2) != sk4
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(component_clause,[status(thm)],[f545]) ).
fof(f548,definition,
! [X3,X4,X5] :
( sQ3_spl
<=> ( app(app(cons(X3,nil),X5),cons(X4,nil)) != sk4
| app(app(cons(X4,nil),X5),cons(X3,nil)) = sk3
| ~ ssList(X5)
| ~ ssItem(X4)
| ~ ssItem(X3) ) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f549,plain,
! [X0,X1,X2] :
( ~ sQ3_spl
| app(app(cons(X0,nil),X2),cons(X1,nil)) != sk4
| app(app(cons(X1,nil),X2),cons(X0,nil)) = sk3
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(component_clause,[status(thm)],[f548]) ).
fof(f551,plain,
( sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f479,f545,f548]) ).
fof(f568,definition,
( sQ8_spl
<=> ssItem(sk11) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f571,plain,
( sQ8_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f489,f545,f568]) ).
fof(f572,definition,
( sQ9_spl
<=> ssItem(sk12) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f575,plain,
( sQ9_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f491,f545,f572]) ).
fof(f576,definition,
( sQ10_spl
<=> ssList(sk13) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f579,plain,
( sQ10_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f493,f545,f576]) ).
fof(f580,definition,
( sQ11_spl
<=> app(app(cons(sk11,nil),sk13),cons(sk12,nil)) = sk2 ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f581,plain,
( ~ sQ11_spl
| app(app(cons(sk11,nil),sk13),cons(sk12,nil)) = sk2 ),
inference(component_clause,[status(thm)],[f580]) ).
fof(f583,plain,
( sQ11_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f495,f545,f580]) ).
fof(f584,definition,
( sQ12_spl
<=> app(app(cons(sk12,nil),sk13),cons(sk11,nil)) = sk1 ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f587,plain,
( ~ sQ12_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f497,f545,f584]) ).
fof(f588,definition,
( sQ13_spl
<=> ssItem(sk5) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f591,plain,
( sQ3_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f498,f588,f548]) ).
fof(f592,definition,
( sQ14_spl
<=> ssItem(sk6) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f595,plain,
( sQ3_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f499,f592,f548]) ).
fof(f596,definition,
( sQ15_spl
<=> ssList(sk7) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f599,plain,
( sQ3_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f500,f596,f548]) ).
fof(f600,definition,
( sQ16_spl
<=> app(app(cons(sk5,nil),cons(sk6,nil)),sk7) = sk2 ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f601,plain,
( ~ sQ16_spl
| app(app(cons(sk5,nil),cons(sk6,nil)),sk7) = sk2 ),
inference(component_clause,[status(thm)],[f600]) ).
fof(f603,plain,
( sQ3_spl
| sQ16_spl ),
inference(split_clause,[status(thm)],[f501,f600,f548]) ).
fof(f608,plain,
( sQ8_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f506,f588,f568]) ).
fof(f609,plain,
( sQ9_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f507,f588,f572]) ).
fof(f610,plain,
( sQ10_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f508,f588,f576]) ).
fof(f611,plain,
( sQ11_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f509,f588,f580]) ).
fof(f612,plain,
( ~ sQ12_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f510,f588,f584]) ).
fof(f625,plain,
( sQ8_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f523,f592,f568]) ).
fof(f626,plain,
( sQ9_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f524,f592,f572]) ).
fof(f627,plain,
( sQ10_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f525,f592,f576]) ).
fof(f628,plain,
( sQ11_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f526,f592,f580]) ).
fof(f629,plain,
( ~ sQ12_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f527,f592,f584]) ).
fof(f630,plain,
( sQ8_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f528,f596,f568]) ).
fof(f631,plain,
( sQ8_spl
| sQ16_spl ),
inference(split_clause,[status(thm)],[f529,f600,f568]) ).
fof(f632,plain,
( sQ9_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f530,f596,f572]) ).
fof(f633,plain,
( sQ10_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f531,f596,f576]) ).
fof(f634,plain,
( sQ11_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f532,f596,f580]) ).
fof(f635,plain,
( ~ sQ12_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f533,f596,f584]) ).
fof(f636,plain,
( sQ9_spl
| sQ16_spl ),
inference(split_clause,[status(thm)],[f534,f600,f572]) ).
fof(f637,plain,
( sQ10_spl
| sQ16_spl ),
inference(split_clause,[status(thm)],[f535,f600,f576]) ).
fof(f638,plain,
( sQ11_spl
| sQ16_spl ),
inference(split_clause,[status(thm)],[f536,f600,f580]) ).
fof(f639,plain,
( ~ sQ12_spl
| sQ16_spl ),
inference(split_clause,[status(thm)],[f537,f600,f584]) ).
fof(f671,plain,
app(nil,nil) = nil,
inference(resolution,[status(thm)],[f315,f249]) ).
fof(f684,plain,
( ~ sQ16_spl
| ssList(sk2)
| ~ ssList(app(cons(sk5,nil),cons(sk6,nil)))
| ~ ssList(sk7) ),
inference(paramodulation,[status(thm)],[f601,f327]) ).
fof(f685,definition,
( sQ17_spl
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f687,plain,
( sQ17_spl
| ~ ssList(nil) ),
inference(component_clause,[status(thm)],[f685]) ).
fof(f692,definition,
( sQ19_spl
<=> ssList(sk2) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f697,definition,
( sQ20_spl
<=> ssList(app(cons(sk5,nil),cons(sk6,nil))) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f700,plain,
( ~ sQ16_spl
| sQ19_spl
| ~ sQ20_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f684,f596,f697,f692,f600]) ).
fof(f715,plain,
! [X0,X1,X2] :
( ~ sQ2_spl
| app(app(cons(X0,nil),cons(X1,nil)),X2) != sk2
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(forward_demodulation,[status(thm)],[f476,f546]) ).
fof(f716,plain,
( ~ sQ16_spl
| ~ sQ2_spl
| ~ ssList(sk7)
| ~ ssItem(sk6)
| ~ ssItem(sk5) ),
inference(resolution,[status(thm)],[f715,f601]) ).
fof(f718,plain,
( ~ sQ16_spl
| ~ sQ2_spl
| ~ sQ15_spl
| ~ sQ14_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f716,f588,f592,f596,f545,f600]) ).
fof(f723,plain,
! [X0,X1,X2] :
( ~ sQ3_spl
| app(app(cons(X0,nil),X2),cons(X1,nil)) != sk4
| app(app(cons(X1,nil),X2),cons(X0,nil)) = sk1
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(forward_demodulation,[status(thm)],[f477,f549]) ).
fof(f724,plain,
! [X0,X1,X2] :
( ~ sQ3_spl
| app(app(cons(X0,nil),X2),cons(X1,nil)) != sk2
| app(app(cons(X1,nil),X2),cons(X0,nil)) = sk1
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(forward_demodulation,[status(thm)],[f476,f723]) ).
fof(f760,plain,
( nil = nil
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f369,f671]) ).
fof(f771,plain,
( ~ sQ16_spl
| nil = app(cons(sk5,nil),cons(sk6,nil))
| ~ ssList(app(cons(sk5,nil),cons(sk6,nil)))
| ~ ssList(sk7)
| sk2 != nil ),
inference(paramodulation,[status(thm)],[f601,f369]) ).
fof(f772,definition,
( sQ22_spl
<=> nil = nil ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f775,plain,
( sQ22_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f760,f685,f772]) ).
fof(f780,definition,
( sQ24_spl
<=> sk7 = nil ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f788,definition,
( sQ26_spl
<=> sk2 = nil ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f801,definition,
( sQ28_spl
<=> nil = app(cons(sk5,nil),cons(sk6,nil)) ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f804,plain,
( ~ sQ16_spl
| sQ28_spl
| ~ sQ20_spl
| ~ sQ15_spl
| ~ sQ26_spl ),
inference(split_clause,[status(thm)],[f771,f788,f596,f697,f801,f600]) ).
fof(f805,plain,
( sQ17_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f687,f249]) ).
fof(f806,plain,
sQ17_spl,
inference(contradiction_clause,[status(thm)],[f805]) ).
fof(f818,plain,
( ~ sQ16_spl
| nil = sk7
| ~ ssList(app(cons(sk5,nil),cons(sk6,nil)))
| ~ ssList(sk7)
| sk2 != nil ),
inference(paramodulation,[status(thm)],[f601,f371]) ).
fof(f830,plain,
( ~ sQ16_spl
| sQ24_spl
| ~ sQ20_spl
| ~ sQ15_spl
| ~ sQ26_spl ),
inference(split_clause,[status(thm)],[f818,f788,f596,f697,f780,f600]) ).
fof(f923,plain,
( ~ sQ3_spl
| ~ sQ11_spl
| app(app(cons(sk12,nil),sk13),cons(sk11,nil)) = sk1
| ~ ssList(sk13)
| ~ ssItem(sk12)
| ~ ssItem(sk11) ),
inference(resolution,[status(thm)],[f581,f724]) ).
fof(f928,plain,
( ~ sQ3_spl
| ~ sQ11_spl
| sQ12_spl
| ~ sQ10_spl
| ~ sQ9_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f923,f568,f572,f576,f584,f580,f548]) ).
fof(f945,plain,
$false,
inference(sat_refutation,[status(thm)],[f551,f571,f575,f579,f583,f587,f591,f595,f599,f603,f608,f609,f610,f611,f612,f625,f626,f627,f628,f629,f630,f631,f632,f633,f634,f635,f636,f637,f638,f639,f700,f718,f775,f804,f806,f830,f928]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC412-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/15.39 % Computer : n008.cluster.edu
% 0.11/15.39 % Model : x86_64 x86_64
% 0.11/15.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/15.39 % Memory : 8046.5625MB
% 0.11/15.39 % OS : Linux 6.8.0-71-generic
% 0.11/15.39 % CPULimit : 300
% 0.11/15.39 % WCLimit : 300
% 0.11/15.39 % DateTime : Mon Sep 21 08:23:41 UTC 2026
% 0.11/15.39 % CPUTime :
% 0.15/15.40 % Drodi V4.1.1
% 0.15/15.42 % Refutation found
% 0.15/15.42 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.15/15.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/15.46 % Elapsed time: 0.053329 seconds
% 0.15/15.46 % CPU time: 0.166904 seconds
% 0.15/15.46 % Total memory used: 110.956 MB
% 0.15/15.46 % Net memory used: 110.796 MB
%------------------------------------------------------------------------------